80
Math
120–10:
Quiz
#7
(thru
3.4)
Name:
Show
as
much
work
as
possible
for
each
problem.
Partial
credit
can
be
earned
for
productive
work
even
if
the
final
answer
is
incorrect.
€
An
unsupported
correct
answer
might
not
receive
full
points.
1.
The
Americans
with
Disabilities
Act
(ADA)
requires,
among
other
things,
that
wheelchair
ramps
1
have
a
slope
of
no
more
than
12
.
(6
points
each)
(a)
Suppose
the
front
steps
of
a
building
are
2.8
feet
high,
and
you
want
to
make
a
ramp
that
conforms
to
the
ADA
standard.
How
far
from
the
building
is
the
base
of
the
ramp?
€
= 1 and
then
asked
what
is
the
run
for
a
rise
of
2.8
feet
Given:
rise
run 12
2.8
1
= 12
⇒ run = 12 2.8 = 33.6 feet So,
run
€
€
(b)
If
you
are
building
a
ramp
that
conforms
to
the
ADA
standard,
and
the
base
of
the
ramp
is
to
be
40
inches
from
the
base
of
the
building,
how
tall
can
the
steps
be?
= 1 and
then
asked
what
is
the
rise
for
a
run
of
40
inches
Given:
rise
run 12
= 1 ⇒ 12rise = 40 ⇒ rise = 40
= 3.3
inches So,
rise
12
40 12
€
€
2.
Give
the
equation
of
the
linear
function
satisfying:
(6
points
each)
( )
(
) (
)
(a)
passes
through
the
points
−1, 7.1 & 4, − 6.4 m=
Δy
Δx
= −6.4−7.1
= −2.7 4−(−1)
€
So,
y + 6.4 = −2.7 x − 4 ⇒ y + 6.4 = −2.7x + 10.8 ⇒ y = −2.7x + 4.4 €
Thus,
f x = −2.7x + 4.4 (
)
()
€
(
)
(b)
passes
through
the
point
4, − 10 and
is
parallel
to
the
line
4 y −2x = 3 €
The
given
line
could
be
rewritten
as
y = 12 x + 43 ,
showing
that
its
slope
is
½.
€
€
Since
our
line
is
to
be
parallel
to
this,
our
slope
is
also
½.
€
So,
y + 10 = 12 x − 4 ⇒ y + 10 = 12 x −2 ⇒ y = 12 x − 12 Thus,
f x = 12 x − 12 €
€
(
()
)
3.
Apples
cost
$0.75
per
pound
and
grapes
cost
$1.25
per
pound.
Let
a
represent
the
number
of
pounds
of
apples
purchased,
and
let
g
represent
the
number
of
pounds
of
grapes
that
are
purchased.
(a)
If
you
have
$6
to
spend
on
fruit,
give
an
equation
that
relates
the
number
of
pounds
of
apples
and
the
number
of
pounds
of
grapes
that
you
can
buy.
(6
points)
0.75a + 1.25g = 6 €(b)
Rewrite
you
answer
to
part
(a)
so
that
we
have
g
as
a
function
of
a.
Write
your
answer
in
the
form
g a = ... (6
points)
()
0.75a + 1.25g = 6 ⇒ 1.25g = −0.75a + 6 ⇒ g = −0.6a + 4.8 €
So,
g a = −0.6a + 4.8 pounds
of
grapes
when
a
pounds
of
apples
are
purchased
€
()
(c)
What
is
the
slope
of
this
function
(including
units)
and
explain
what
it
means
in
the
€
context
of
this
problem.
(6
points)
slope
=
‐0.6
pounds
of
grapes
per
pound
of
apples
For
each
additional
pound
of
apples
purchased,
0.6
fewer
pounds
of
grapes
must
be
purchased.
4.
Determine
whether
each
of
the
following
tables
represent
a
linear
function.
If
it
does
not,
show
work
to
support
that
conclusion.
If
it
does,
also
give
the
function’s
formula.
(8
points
each)
(a)
x
y
‐2
‐28.2
1
‐7.8
3
5.8
8
39.8
10
53.4
−7.8−(−28.2)
1−(−2)
39.8−5.8
8−3
= 6.8
= 6.8
5.8−(−7.8)
3−1
= 6.8
53.4−39.8
10−8
= 6.8
€
Since
all
are
equal,
it
is
a
linear
function,
and
then
we
have:
y −5.8 = 6.8 x −3 ⇒ y −5.8 = 6.8x −20.4 ⇒ y = 6.8x − 14.6 So,
f x = 6.8x − 14.6 €
€
(
()
)
(b)
x
y
3
9
7−3
7
24
Since
these
are
not
equal,
it
is
not
a
linear
function.
9
34
20
80
24−9
= 3.75
34−24
9−7
€
= 5
5.
A
scientist
collected
the
following
data
on
the
speed,
S,
in
centimeters
per
second,
at
which
ants
ran
at
various
temperatures,
T,
measured
in
°C.
Temperature
(T)
25.6
27.5
30.3
30.4
32.2
33.0
33.8
Speed
(S)
2.62
3.03
3.57
3.56
4.03
4.17
4.32
(a)
Find
the
linear
regression
model
for
the
data
giving
S
as
a
function
of
T.
(6
points)
€
()
S T = 0.209T −2.729 cm
per
second
at
a
temperature
of
T°C
(b)
Explain
the
meaning,
in
this
context,
of
the
slope
of
the
regression
line.
(6
points)
For
each
1°C
increase
in
temperature,
the
running
speed
of
the
ants
will
increase
by
about
0.209
cm
per
second.
(c)
Express,
in
function
notation,
the
speed
at
which
the
ants
run
when
the
temperature
is
29°C
and
when
the
temperature
is
40°C,
and
then
estimate
these
values.
Which
is
a
more
reliable
estimate?
Explain?
(10
points)
S 29 = 3.32cm
per
second
€
S 40 = 5.62cm
per
second
Since
29°C
is
within
the
scope
of
the
original
data,
the
estimate
at
this
temperature
is
more
likely
to
be
reliable.
€
( )
( )